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本文探讨非线性声速分布、内波扰动、和海底反射对哈密顿抛物射线方程动力学行为的影响。运用Poincare映象、Lyapunov指数等非线性动力学方法对射线系统行为进行描述。结果显示水声射线在不发生海底反射的情况下,内波对声速扰动的增强将导致正的Lyapunov指数,使射线产生不规则的混沌运动并扩大射线系统的混沌区域。然而海底反射显著影响了声速分布、内波扰动和射线运动的非线性相互作用。海底深度的减小使声射线系统的混沌区域扩大,然而过小的深度减弱了声速分布和射线的非线性相互作用,使混沌区域缩小。因此,我们可以得出海底反射对于水声射线的混沌动力学行为有重要影响的结论。
In this paper, the effects of nonlinear velocity distribution, internal-wave perturbation and sub-sea reflection on the dynamics of the Hamilton parabolic equation are discussed. Ray system behavior is described using Poincare maps, Lyapunov exponents and other nonlinear dynamics methods. The results show that the enhancement of the sound wave velocity disturbance caused by the underwater acoustic wave will lead to a positive Lyapunov exponent without the occurrence of seafloor reflection, which will make the ray produce irregular chaotic motion and enlarge the chaotic region of the ray system. However, the seafloor reflections significantly affect the nonlinear interaction of sound velocity distribution, internal wave perturbation and ray motion. The decrease of seafloor depth enlarges the chaotic area of acoustic ray system, but the too small depth weakens the nonlinear interaction between sound velocity distribution and ray, and reduces the chaotic area. Therefore, we can draw the conclusion that the seabed reflection has an important influence on the chaotic dynamic behavior of the acoustic acoustic radiation.